15n^2-7np-2p^2=0

Solution for 15n^2-7np-2p^2=0 equation:

Simplifying
15n2 + -7np + -2p2 = 0

Reorder the terms:
-7np + 15n2 + -2p2 = 0

Solving
-7np + 15n2 + -2p2 = 0

Solving for variable 'n'.

Factor a trinomial.
(3n + -2p)(5n + p) = 0

Subproblem 1
Set the factor '(3n + -2p)' equal to zero and attempt to solve:

Simplifying
3n + -2p = 0

Solving
3n + -2p = 0

Move all terms containing n to the left, all other terms to the right.

Add '2p' to each side of the equation.
3n + -2p + 2p = 0 + 2p

Combine like terms: -2p + 2p = 0
3n + 0 = 0 + 2p
3n = 0 + 2p
Remove the zero:
3n = 2p

Divide each side by '3'.
n = 0.6666666667p

Simplifying
n = 0.6666666667p
Subproblem 2
Set the factor '(5n + p)' equal to zero and attempt to solve:

Simplifying
5n + p = 0

Solving
5n + p = 0

Move all terms containing n to the left, all other terms to the right.

Add '-1p' to each side of the equation.
5n + p + -1p = 0 + -1p

Combine like terms: p + -1p = 0
5n + 0 = 0 + -1p
5n = 0 + -1p
Remove the zero:
5n = -1p

Divide each side by '5'.
n = -0.2p

Simplifying
n = -0.2p
Solution
n = {0.6666666667p, -0.2p}